https://doi.org/10.48550/arXiv.2312.12623
Summary
Non-blazar AGN PKS 0521-36 observed over 15 years by Fermi-LAT telescope.
Lomb-Scargle and wavelet analysis reveals three Quasi-periodic oscillations (QPOs).
GP modelling revealed two more QPOs.
First
long-term QPO detected from a non-blazar AGN.
Cause of QPOs remains unclear.
Evidence for QPOs seems inconsistent.
Data
ROI is circular region of 10
\(^\circ\)
radius centred at PKS 0521-36
15 years of observations by Fermi-LAT (August 2008 - 2023)
MJD 54683 – MJD 60187 (5,504 days)
\(\gamma\)
-ray light curve (0.1 – 300 GeV)
Uniformly sampled
Method
Compute Lomb-Scargle periodogram.
Compute Weighted wavelet Z-transform.
Fit Gaussian Process model with different kernels:
Damped Random Walk,
Simple Harmonic Oscillator, and
combinations thereof.
Choose best kernel combination using BIC.
Look for “significant” peaks in power.
“Significance” estimation
Nice application of bootstrapping to get the distribution of light curves.
Not clear how
\(\beta = 0.48 \pm 0.16\)
is determined.
Results: LSP and WWZ
T = 268, 295, 806 days.
Results: GP Model
Results: GP PSD
Statistical Comments
CARMA is a
stochastic
process
CAR(1) is a special case that can be expressed as GP.
Computationally heavy, N
\(\approx\)
500, 32 chains, 15000 steps.
No mention of priors.
Where does the “quasi” come from?
LSP and WWZ target periodicity, not quasi-periodicity.
Why not use QP GP kernels.
[Aside] More data
\(\rightarrow\)
more likely to reach significance.
3
\(\sigma\)
vs. 5
\(\sigma\)
might not itself be significant.
Note on BIC
\[\textrm{BIC} = -2\mathcal{L} + K \log N\]
BIC should only be used to compare between models that are subsets of eachother.
Not surprising that BIC increases with model complexity.
Manuscript queries
QPOs don’t match between LSP/WWZ and GP models
\(T = 268, 295, 806\)
days vs.
\(T = 283, 886\)
days.
Used different date ranges MJD 54683 – 60187 (15y) vs. MJD 55358 – 59547 (11.4y) for each.
Kelly et al. (2009) and Li & Wang (2018) are analyses of optical not
\(\gamma\)
-ray light curves.
Insufficient information to reproduce, e.g., source code.
QPO vs BH Mass